This is the second competitive renewal of a grant to develop, test, and apply methods used to study the genetic epidemiology of common disease. The previous grant period was very productive. Among other things we; 1) Showed that it was possible to infer the correct mode of inheritance and penetrance from linkage data, by maximizing lod scores; 2) Demonstrated that if a disease is determined by two epistatically interacting loci, one of which is linked to a marker, the effect of the second locus on linkage analysis can be subsumed under "reduced penetrance" with little bias or loss of power in the linkage results; 3) Showed that mode of inheritance can be determined from linkage data even in the presence of heterogeneity; 4) Found that a common form of epilepsy is linked to the HLA locus on chromosome 6 and that the most likely mode of inheritance is two-locus; 5) Found negative evidence for linkage of thyroid disease to HLA, despite an association between HLA and thyroid disease. Much of the research supported by this grant has used simulation approaches to test existing methods and to develop new analysis techniques. When it was first funded, this grant was one of the few that supported development of computer simulation approaches as a tool in the study of genetic epidemiology. In this proposal, I continue to use both analytic and computer simulation methods to develop new ways of looking at inheritance in disease populations and apply the new methods to disease data. The proposal has 4 main areas of investigation: 1. Continued investigation of linkage analysis when the disease is oligogenic; particularly, investigating the theoretical and actual differences in doing "correct" vs "incorrect" two locus analysis; 2. Using lod scores to determine mode of inheritance (MMLS) method): constructing significance levels to determine the reliability of inferences bases on the MMLS method, especially when heterogeneity is present; 3. Linkage strategies: Within-family heterogeneity; heterogeneity and unknown mode of inheritance; the informativeness os a family; the sensitivity of lod scores to changes in the phenotype; 4. Ascertainment problems in large pedigrees; doing linkage analysis to a "risk factor: or associated marker. The recent spectacular successes in molecular biology have been almost exclusively in diseases whose genetic have been known for decades. The population genetic characteristics of relatively common diseases such as diabetes, thyroid disease, ulcer, etc., remain obscure, partly because the genetic analysis methodology available to study disease populations has proven inadequate. The work proposed here will, as with past work, expand our repertoire of methods used to study genetic disease.